EduSahara™ Worksheet

Question 1

1.

A chord that passes through the centre of the circle is called

(i)

semi-circle
(ii)

circumference
(iii)

diameter
(iv)

centre
(v)

radius

Question 2

2.

A chord of a circle divides the whole circular region into two parts, each called a

(i)

segment
(ii)

semi-circle
(iii)

chord
(iv)

diameter
(v)

major segment

Question 3

3.

The segment of the circle containing the centre of the circle is called

(i)

diameter
(ii)

circumference
(iii)

major segment
(iv)

segment
(v)

radius

Question 4

4.

Which of the following statements are true?

a)	Each radius of a circle is also a chord of the circle.
b)	A line can meet a circle atmost at two points.
c)	Every circle has a unique centre.
d)	A circle consists of an infinite number of points.
e)	Every circle has a unique diameter.

(i)

{a,b}
(ii)

{a,b,c}
(iii)

{b,c,d}
(iv)

{e,c}
(v)

{a,e,d}

Question 5

5.

Which of the following statements are true?

a)	Two semi-circles of a circle together make the whole circle.
b)	Every circle has a unique diameter.
c)	An infinite number of diameters may be drawn for a circle.
d)	An infinite number of chords may be drawn for a circle.
e)	One and only one tangent can be drawn to a circle from a point outside it.

(i)

{b,e,d}
(ii)

{e,c}
(iii)

{a,c,d}
(iv)

{b,a}
(v)

{b,a,c}

Question 6

6.

In the given triangle S is the circumcentre. If SE = 13.40 cm, find the circumference of the circumcircle

(i)

84.2 cm
(ii)

85.2 cm
(iii)

83.2 cm
(iv)

82.2 cm
(v)

86.2 cm

Question 7

7.

Find the side of the square in the following figure if the radius of the circle is 12.00 cm.

(i)

15.97 cm
(ii)

14.97 cm
(iii)

18.97 cm
(iv)

16.97 cm
(v)

17.97 cm

Question 8

8.

If a chord DE = 14 cm is drawn in a circle with radius OD = 10 cm, find its distance from the centre of the circle

(i)

5.14 cm
(ii)

8.14 cm
(iii)

6.14 cm
(iv)

9.14 cm
(v)

7.14 cm

Question 9

9.

The diameter FG of a circle with centre 'O' is perpendicular to the chord DE. If DE = 18.00 cm and FH = 3.45 cm, find the radius of the circle.

(i)

15.45 cm
(ii)

13.45 cm
(iii)

14.45 cm
(iv)

11.45 cm
(v)

12.45 cm

Question 10

10.

'C' and 'D' are centres of circles of radii 4 cm and 11 cm such that CD = 17 cm and 'E' is the centre of the circle of radius 'r' cm which touches the above circles externally. If ∠CED = 90°, find 'r'

(i)

4 cm
(ii)

6 cm
(iii)

5 cm
(iv)

2 cm
(v)

3 cm

Question 11

11.

Which of the following statements are true?

a)	Atmost one chord can be drawn on a circle with a certain length.
b)	The diameter is the longest chord.
c)	A chord divides a circle into two sectors.
d)	The radius is the shortest chord.
e)	A chord divides a circle into two segments.

(i)

{b,e}
(ii)

{c,e,b}
(iii)

{a,b}
(iv)

{c,e}
(v)

{d,a,b}

Question 12

12.

Which of the following statements are true?

a)	Equal length chords are equidistant from the centre of the circle.
b)	Equal length chords subtend equal angles at the centre of the circle.
c)	The farther the chord is from the centre, the larger the angle it subtends at the centre.
d)	No two chords bisects each other.
e)	The longest chord of the circle passes through the centre of the circle.

(i)

{d,b}
(ii)

{c,d,e}
(iii)

{a,b,e}
(iv)

{c,a,b}
(v)

{c,a}

Question 13

13.

Which of the following statements are true?

a)	The area enclosed by a chord and its major arc is called major segment.
b)	A sector is the area enclosed by two radii and a chord.
c)	The area enclosed by a chord and its minor arc is called minor segment.
d)	A circle divides the plane on which it lies into three parts.
e)	The diameter divides the circle into two unequal parts.

(i)

{b,a,c}
(ii)

{b,e,d}
(iii)

{b,a}
(iv)

{a,c,d}
(v)

{e,c}

Question 14

14.

Which of the following statements are true?

a)	Two chords bisect each other.
b)	The longest of all chords of a circle is called diameter.
c)	The diameter divides the circle into two unequal parts.
d)	The midpoint of any diameter of a circle is its centre.
e)	A sector is the area enclosed by two radii and a chord.

(i)

{b,d}
(ii)

{c,d,b}
(iii)

{a,b}
(iv)

{e,a,b}
(v)

{c,d}

Question 15

15.

Which of the following statements are true?

a)	A diameter is a limiting case of a chord.
b)	A tangent is the limiting case of a secant.
c)	A secant has two end points.
d)	A secant and a chord are same.
e)	A radius is a limiting case of a diameter.

(i)

{a,b}
(ii)

{d,b}
(iii)

{d,b,a}
(iv)

{c,a}
(v)

{e,c,a}

Question 16

16.

EF , GH , IJ , KL are chords of a circle with EF = 8 cm , GH = 4 cm , IJ = 5.1 cm and KL = 7.09 cm. The chord farthest from the centre of the circle is

(i)

EF = 8 cm
(ii)

IJ = 5.1 cm
(iii)

GH = 4 cm
(iv)

KL = 7.09 cm

Question 17

17.

In the given figure, F and G are centres of two circles with equal radii intersecting at H and I. If FG = 20 cm and HI = 18.2 cm, find the radii of the circles

(i)

11.52 cm
(ii)

12.52 cm
(iii)

13.52 cm
(iv)

15.52 cm
(v)

14.52 cm

Question 18

18.

In the given figure, two circles of radii AC = 13.9 cm & BC = 10.7 cm intersect at C & D. The distance between the centres AB = 20 cm, find the length of CD

(i)

16.14 cm
(ii)

13.14 cm
(iii)

14.14 cm
(iv)

12.14 cm
(v)

15.14 cm

Question 19

19.

In the given figure, O is the centre of the circle. I is a point on chord GH such that GI = IH. Find ∠OIG

(i)

95°
(ii)

90°
(iii)

120°
(iv)

100°
(v)

105°

Question 20

20.

BC is a line segment and E is its mid-point. Three semi-circles are drawn with BE , EC and BC as diameters. D , F and E respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given BD = 5 cm